The simile "as RIGHT as rain" is idiomatic in English. Is there an idiomatic equivalent for "wrong"? If so what is it? If not, any suggestions?
If what you are looking for is an idiom for a state of ultimate wrongness, rather than a direct negative equivalent of 'Right as rain', then you might consider 'Wrong as wrong can be'. There is no simile involved, but it shares a similar structure and delivers the sense of an absolute state of wrongness which you are seeking.
The earliest dated "as wrong as" simile I could find in U.S. sources was from a collection of similes listed in Rian James, "The Inky Way," in the Brooklyn [New York] Daily Eagle (February 9, 1930):
As wrong as an ambulance surgeon's diagnosis.
but that lacks the simplicity and rhythm needed to become a commonplace. Much more promising is this one from several online websites, including Encyclopedia.com:
As wrong as sin on Sunday.
But I also like the implication of this one from AskReddit:
As wrong as two left feet.
which is essentially the same answer that Hank offered earlier (his uses shoes instead of feet, but either way they aren't right).
Old, regional, and presumably obsolete, but nonetheless intriguing (because it contributes to an odd interpretation of a very familiar idiomatic phrase) is this one from John Hotten, A Dictionary of Modern Slang, Cant, and Vulgar Words, second edition (1860):
As wrong as a bucket.
Hotten suggests its relevance in an entry for "kick the bucket":
KICK THE BUCKET, to die.—Norfolk. According to Forby, a metaphor taken from the descent of a well or mine, which is of course absurd. The Rev. E. S. Taylor supplies me with the following note from his Ms. additions to the work of the East-Anglian lexicographer:—
The allusion is to the way in which a slaughtered pig is hung up,—viz., by passing the ends of bent piece of wood behind the tendons of the hind legs, and so suspending it to a hook in a beam above. This piece of wood is locally termed a bucket, and so by a coarse metaphor the phrase came to signify to die. Compare the Norfolk phrase, "as wrong as a bucket."
I couldn't find any mention of "as wrong as a bucket," although Robert Forby, The Vocabulary of East-Anglia, volume 1 (1830) confirms the meaning of bucker ("sometimes pronounced Bucket") as being "A bent piece of wood somewhat like it [a hors's hind leg] in shape; particularly that on which a slaughtered animal is hung up, more generally called a gambrel."
I see two problems with this question:
1) "Right" in the expression "right as rain" is not a relational opposite to "wrong."
2) There are an overabundance of "wrong" idiomatic similes (easily found with the help of a certain search engine that rhymes with stroogle).
The structure has been a creative template for all sorts of expressions. Here's a sampling:
as wrong as a three-dollar bill
as wrong as a Playboy magazine sitting on the pew of a Catholic church next to the hymnal (Sherry Riter)
"The official version of Watergate is as wrong as a Flat Earth Society pamphlet." - G. Gordon Liddy
For the best idiomatic simile that is a relational opposite to "right as rain" in meaning (without "wrong"), there is sick as a dog.
"As bad as the itch" seems to be suitable.
If you are looking for a phrase which compares levels of wrongness 'wronger than wrong' is worth consideration. It is a term coined by Isaac Asimov in his book of essays The Relativity of Wrong.
A statement that equates two errors is wronger than wrong when one of the errors is clearly more wrong than the other. As Asimov put it:
When people thought the Earth was flat, they were wrong. When people thought the Earth was spherical, they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together.